. A treatise on plane and spherical trigonometry, and its applications to astronomy and geodesy, with numerous examples . B + C)] (Art. 198) - sing sin j-B sin^-C sin^-Awhich in (1) gives . B . C sm — sm — 2 2tan r = —- —— sin a (3) cos|-A v y . (Art. 196) (4) 2 cos f A cos -J-B cos -J-Can equation which is equivalent to the following : cotr = —[cosS + cos(S-A)+cos(S-B)+cos(S-C)](5) u JN 216. The Ex-Circles. — To find the angular radii of theex-circles of a triangle. A circle which touches one side of a triangle and theother two sides produced, is called an escribed circle, orex-circle, of the
. A treatise on plane and spherical trigonometry, and its applications to astronomy and geodesy, with numerous examples . B + C)] (Art. 198) - sing sin j-B sin^-C sin^-Awhich in (1) gives . B . C sm — sm — 2 2tan r = —- —— sin a (3) cos|-A v y . (Art. 196) (4) 2 cos f A cos -J-B cos -J-Can equation which is equivalent to the following : cotr = —[cosS + cos(S-A)+cos(S-B)+cos(S-C)](5) u JN 216. The Ex-Circles. — To find the angular radii of theex-circles of a triangle. A circle which touches one side of a triangle and theother two sides produced, is called an escribed circle, orex-circle, of the triangle. It is clear that the three ex-circlesof any triangle are the in-circles of its colunar triangles(Art. 191, Sch.). Since the circle escribed to the side a of the triangleABC is the in-circle of the colunar triangle ABC, the partsof which are a, -n- — b, ir — c,A, 7r — B, 7r — C, the problembecomes identical with thatof Art. 215; and we obtainthe value for the in-radius ofthe colunar triangle ABC, by substituting for 6, c, B, C,their supplements in the five equations of that
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Keywords: ., bookcentury1900, bookdecade1900, booksubjecttrigono, bookyear1902
